Lecture 6

Fundamentals of Physics

Phys 120, Fall 2014

Energy

A. J. Wagner

North Dakota State University, Fargo, ND 58102

Fargo, September 10, 2015

Overview

• Doing work

• Helmholtz “living force”

• Defining an energy for mechanical systems

• Work and Energy

• Gravitational energy

• Other forms of energy

• Power

1

Doing work

As the development of machines increased in

the 17th century it became important to under-

stand the power these machines had in practi-

cal terms? How much work could they perform.

And how would you quantify work?

A practical and simple measure of work turned

out to be the height to which a weight could be

raised. It turns out that, as long as you use a

slow an steady motion, you find that a machine

can raise a weight to a certain height, wheras

double the weight could only be raised only half

the distance.

This corresponds to the force required to raise

the weight times the distance it will be raised,

i.e.

W = F · d

2

Work

Physicists definition: work is done whenever an object is pushed or pulled

through a distance.

More precisely: object A does work on object B is A exerts a force on B while

B mores in the direction of that force∗.

∗We won’t consider the situation where motion and force don’t align here.

3

Concept check

I lie on the floor in a relaxed state. Do I perform any work?

I hold myself in a painful push-up position. Do I perform any work?

I push the table across the floor at a constant speed. Do I perform any work?

4

Work defined quantitatively

work = force× distance

or

w = Fd

The units of work are Nm = J also called a Joule.

5

Concept check

I lift a 5kg chair over a distance of 2m (slowly and at constant speed).

1. No work is done.

2. 5 J of work are done.

3. 10 J of work are done.

4. 50 J of work are done.

5. 100 J or work are done.

6

Industrial revolution

Steam engines became practical at the end of the 18th century.

This fueled the industrial revolution. Starting in England manufacturing gets

rationalized and factories develop. City populations grow and “for the first time

in history, the living standards of the masses of ordinary people have begun to

undergo sustained growth”∗.

This also lead to a different perspective on physical processes and technology

influences the directions of scientific thought.∗Lucas, Robert E., Jr. (2002). Lectures on Economic Growth. Cambridge: Harvard UniversityPress. pp. 10910

7

Carnot

Steam engines had been invented by practical inventers,

but much of the physics behind the operation of such

a machine was unknown.

Sadi Carnot was the first person to really consider the

theory of a steam engine carefully. His only publica-

tion Reflections on the Motive Power of Fire was both

a breakthrough in the understanding of work and trans-

formation of energy, and at the same time almost com-

pletely ignored.

Lord Kelvin (born William Thompson) rediscovered

Carnot’s results and later credited Carnot with the in-

vention of the new science called “thermodynamics”.

Much more about that in the next lecture.

Sadi Carnot

born 1796

died 1832

8

Helmholtz

Hermann v. HelmholtzPhysicianPhysicist*1821, †1894

Hermann Ludwig Ferdinand von Helmholtz was a Ger-

man physician and physicist who made significant

contributions to several widely varied areas of modern

science.

Here we are interested in his observation of the heat-

ing up of decomposing bodies. Where did that heat

come from? He followed the ancient Greek thesis

“nothing comes from nothing” and decided that the

heat must come from some other “living force” re-

siding in the material and that this force gets trans-

formed but not created or destroyed. We now call

this “living force” energy.

He was able to show that for Newton’s mechanics this

could be given a specific definition.

9

Newton’s mechanics and kinetic energy

If I lift up a book I need to do work equal to the distance times the weight of

the book or Ep = mgh. This work that I do to the book is still there, since I can

use this book to lift something else. This form of energy is called potential

energy.

If I drop the book, what is happening to the potential energy?

It obtains speed!

It gets transformed into another from of energy which we call kinetic energy.

This is the energy the book has due to its speed. How much kinetic energy

does a book have after it has fallen? Exactely the same amount as the original

potential energy.

10

Quantiative expression for kinetic energyFrom lecture 3 we know that for uniformly accelerate motion

x(t) = h−

1

2gt2 (1)

So the time when x = 0 is given by

t =

√

2h

g(2)

and the velocity is then given by

v = gt = g

√

2h

g=

√

2gh (3)

But E = mgh, so gh = E/m and we get

v =

√

2E

m(4)

which we can rewrite as

kinetic energy =

(

1

2

)

× (object’s mass)× (square of object’s speed)

or

Ek =1

2mv2

This kinetic energy is defined such that (neglecting air resistance) the gravita-

tional energy at the beginning gets exactly transformed into kinetic energy at

the end.

11

Concept check

I drop a 1kg weight from a height of 1 m to the floor.

What is the initial potential energy (wrt the floor)?

(a) 0; (b) 10 J; (c) 1 J; (d) 10 N;

What is the initial kinetic energy?

(a) 0; (b) 10 J; (c) 1 J; (d) 10 N;

What is the kinetic energy just before the book hits the floor?

(a) 0; (b) 10 J; (c) 1 J; (d) 10 N;

What if the potential energy just before the book hits the floor?

(a) 0; (b) 10 J; (c) 1 J; (d) 10 N;

What about after it has hit the floor?

12

Concept check

How much kinetic energy do I have if I run with 2m/s compared to when I run

with 1 m/s?

(a) the same kinetic energy;

(b) twice the kinetic energy;

(c) four times the kinetic energy;

(d) eight times the kinetic energy;

13

Concept check

If I throw a ball up with a velocity of 10 m/s it will rise to a height of 5 m.

How fast do I have to throw the ball so that it will rise to a height of 10 m?

(a) 10 m/s;

(b) 20 m/s;

(c) 30 m/s;

(d) 40 m/s;

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Energy conservation

So far we have neglected air resistance, and that is clearly not always a good

approximation. Helmholtz was thinking about a much deeper concept of al-

ways conserving energy.

There are different kinds of energy: gravitational energy, kinetic energy, elas-

tic energy, thermal energy, electromagnetic energy, radiant energy, chemical

energy, nuclear energy.

15

Joule’s energy conservation: 1847 lecture

You see, therefore, that living force (kinetic energy) may be con-verted into heat, and that heat may be converted into living force,or its equivalent attraction through space. All three therefore —namely, heat, living force, and attraction through space (to whichI might also add light, were it consistent with the scope of thepresent lecture) – are mutually convertible into one another. Inthese conversions nothing is lost . . . . We can therefore expressthe equivalence in definite language applicable at all times and un-der all circumstances. Thus the attraction of 817 lb. through thespace of one foot is equivalent to, and convertible into, the livingforce possessed by a body of the same weight of 817 lb. whenmoving with the velocity of eight feet per second, and this liv-ing force is again convertible into the quantity of heat which canincrease the temperature of one pound of water by one degreeFahrenheit.

James Prescott Joule

born 1818

died 1889

16

Law of conservation of Energy

The total energy of all participants in any process remains unchanged through-

out that process. That is, energy cannot be created or destroyed. Energy can

be transformed (changed from one form to another), and it can be transferred

(moved from one place to another), but the total amount stays always the

same.

This law is as true as any general rule ever gets. It is correct in any situation

yet observed. It even holds where Newton’s laws are no longer applicable.

17

Definition of Potential energy

Define the potential energy of an object as the amount of work it takes to

bring the object to a certain height:

gravitational energy = weight× height∗

You can use that energy to do work.

∗Where the height is measured from some reference point, e.g. the floor.

18

Work-Energy principle

Work is an energy transfer. Work reduces the energy of the system doing the

work and increasing the energy of the system on which work is done, both by

an amount equal to the work done.

19

Energy conservation in β -decay

When scientists observed β-decay (a nucleus emits an electron) it was observed

that energy was not conserved.

Maybe there was a new particle? Tried to capture this in lead, but no success.

This was the situation of 1914 - 1930. By 1929 physicists like Niels Bohr

suggested that maybe energy was not conserved in nuclear reactions.

Wolfgang Pauli hypotesized a particle that interacted so weakly that it could

not be captured in the lead. It was eventually found (more about that in a

later lecture) and called the neutrino.

20

True story about a Fargo inventor

About a year ago I was visited by a Fargo inventor that had developed (con-ceptually) a machine that will solve our energy problems by generating energyin a renewable process that needed not external fuel cell. He was looking forfunding from the Navy for his research.

Would you write him a letter of support?

I met him later and he told me that he had been successful in obtaining funding for his research.

21

Energy efficiency

Often only a small part of the energy can be transformed to do useful energy.

Think of using the chemical energy in a sandwich to carry a chair upstairs. We

define energy efficiency as:

Energy efficiency =useful output energy

total input energy

It is usually expressed as a percentage. The efficiency of a typical human

muscular activity is only about 10%.

22

Power

What is the difference between walking and running up a flight of stairs? The

same amount of work is done, but there is a difference:

power =work done

time to do it

The unit is J/s = W or a Watt.

23

Estimates

What is your power output while running up a flight of stairs?

If the energy efficiency of this process is 10%, what is your (chemical) power

input?

24

Concept check

You press a 500N weigh from the shoulders up to arms’ length, a distance of

0.8m during a period of 2 seconds.

How much work did you do?

What is your power output?

25

Timeline1500 1920

1600 1700 1800 1900

Galileo Industrial Revolution

Descartes

Newton

Leibniz

Kepler

Carnot

Helmholtz

Joule

Kelvin

26

Summary

• Work = Fd

• Kinetic energy Ek = (1/2)mv2

• Gravitational energy Eg = mgh

• Law of energy conservation

• Work energy principle

• Forms of energy

• efficiency & power

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